--- name: kolmogorov-arnold-networks-guide-9ea8517c7ffe description: "Papers and tutorials on KAN learnable activation networks" metadata: openclaw: emoji: "📐" category: "domains" subcategory: "ai-ml" keywords: ["KAN", "Kolmogorov-Arnold", "learnable activations", "spline networks", "neural architecture", "interpretability"] source: "https://github.com/mintisan/awesome-kan" --- # Kolmogorov-Arnold Networks (KAN) Guide ## Overview Kolmogorov-Arnold Networks (KANs) are a novel neural network architecture that places learnable activation functions on edges (weights) instead of fixed activations on nodes. Based on the Kolmogorov-Arnold representation theorem, KANs use B-spline functions as learnable edge activations, achieving better accuracy and interpretability than MLPs with fewer parameters in certain domains. This collection tracks the rapidly growing KAN literature. ## Core Concept ``` Traditional MLP: x → [fixed activation(linear transform)] → y Activations on nodes, weights on edges KAN: x → [learnable spline functions on edges] → sum → y Each edge learns its own activation function (B-spline) Kolmogorov-Arnold Theorem: f(x₁,...,xₙ) = Σ Φᵢ(Σ φᵢⱼ(xⱼ)) Any multivariate continuous function = composition of univariate functions and addition ``` ## Key Papers ```bibtex @article{liu2024kan, title={KAN: Kolmogorov-Arnold Networks}, author={Liu, Ziming and Wang, Yixuan and Vaidya, Sachin and Ruehle, Fabian and Halverson, James and Solja{\v{c}}i{\'c}, Marin and Hou, Thomas Y. and Tegmark, Max}, journal={arXiv:2404.19756}, year={2024} } ``` ## Implementation ```python # Using pykan (official implementation) # pip install pykan from kan import KAN import torch # Create a KAN model model = KAN( width=[2, 5, 1], # Input: 2, Hidden: 5, Output: 1 grid=5, # Spline grid resolution k=3, # Spline order (cubic) ) # Training data x = torch.randn(1000, 2) y = torch.sin(x[:, 0]) + torch.cos(x[:, 1]) y = y.unsqueeze(1) # Train dataset = {"train_input": x[:800], "train_label": y[:800], "test_input": x[800:], "test_label": y[800:]} model.train(dataset, steps=100, lr=0.01) # Visualize learned functions model.plot() # Prune and simplify model = model.prune() model.plot() ``` ## KAN vs MLP Comparison ```python # Comparison on function approximation from kan import KAN import torch.nn as nn # KAN: learnable activations on edges kan_model = KAN(width=[2, 5, 1], grid=5, k=3) # Parameters: ~150 (spline coefficients) # MLP: fixed activations on nodes class MLP(nn.Module): def __init__(self): super().__init__() self.net = nn.Sequential( nn.Linear(2, 50), nn.ReLU(), nn.Linear(50, 50), nn.ReLU(), nn.Linear(50, 1), ) def forward(self, x): return self.net(x) mlp_model = MLP() # Parameters: ~2,700 # KAN advantages: # - Fewer parameters for same accuracy # - Interpretable (visualize learned functions) # - Better for scientific discovery (symbolic regression) # - Grid refinement for progressive accuracy # MLP advantages: # - Faster training # - Better scaling to high dimensions # - More mature tooling and optimization ``` ## Extensions and Variants | Variant | Innovation | Application | |---------|-----------|-------------| | **KAN 2.0** | MultKAN with multiplication nodes | Improved scaling | | **Temporal KAN** | Time-series adaptation | Forecasting | | **ConvKAN** | KAN + convolutions | Image processing | | **GraphKAN** | KAN on graph structures | Graph learning | | **FourierKAN** | Fourier basis instead of splines | Periodic functions | | **WavKAN** | Wavelet-based activations | Signal processing | | **BSRBF-KAN** | B-spline + radial basis | Function approximation | ## Scientific Applications ```python # KAN for symbolic regression (discovering equations) from kan import KAN # Generate data from unknown equation: f(x,y) = x*exp(y) import torch x = torch.rand(1000, 2) * 2 y = x[:, 0:1] * torch.exp(x[:, 1:2]) dataset = {"train_input": x[:800], "train_label": y[:800], "test_input": x[800:], "test_label": y[800:]} model = KAN(width=[2, 1, 1], grid=10, k=3) model.train(dataset, steps=200) # Symbolic fitting — discover the equation model.auto_symbolic() # Output: f(x₁, x₂) = x₁ * exp(x₂) # KAN can discover symbolic expressions from data ``` ## Research Landscape ```markdown ### Key Research Directions 1. **Scaling** — Making KANs work at LLM scale 2. **Efficiency** — Reducing spline computation overhead 3. **Theory** — Understanding approximation guarantees 4. **Architecture search** — Optimal KAN topologies 5. **Hybrid models** — Combining KAN and MLP strengths 6. **Domain applications** — Physics, chemistry, biology 7. **Interpretability** — Extracting symbolic knowledge ``` ## Use Cases 1. **Scientific discovery**: Extract equations from experimental data 2. **Function approximation**: High-accuracy low-parameter models 3. **Interpretable ML**: Understand what the network learned 4. **Physics-informed**: Embed physical constraints in activations 5. **Education**: Teach alternative neural network architectures ## References - [awesome-kan](https://github.com/mintisan/awesome-kan) - [KAN Paper](https://arxiv.org/abs/2404.19756) - [pykan Implementation](https://github.com/KindXiaoming/pykan) - [KAN 2.0 Paper](https://arxiv.org/abs/2408.10205) --- Source attribution: wentorai Original project: https://github.com/wentorai/research-plugins/blob/bf44b3cd617fa94c8a1b254c5d1987142ca3d631/skills/domains/ai-ml/kolmogorov-arnold-networks-guide/SKILL.md License: MIT License information: https://opensource.org/license/mit Original upstream instructions; downloaded from Mega AI Hub. ## Upstream license notice MIT License Copyright (c) 2026 Wentor AI Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. # Mega AI Hub resource metadata Creator / publisher: wentorai Original project: https://github.com/wentorai/research-plugins/blob/bf44b3cd617fa94c8a1b254c5d1987142ca3d631/skills/domains/ai-ml/kolmogorov-arnold-networks-guide/SKILL.md Attribution basis: Source repository record Fields of work: Data & Analytics, Development & Engineering, Education & Research Roles: Data Scientist, ML / AI Engineer, Researcher Specialties: API Tools: Pykan Country applicability: Country not specified Classification basis: Source catalog labels Instruction SHA-256: 7ba7d885489d5a78e0c62f71af97ea73b7ed59958ee03ffb02e104c2d1800423